Title

Author

Date of Award

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Jiu-Kang Yu

Second Advisor

Freydoon Shahidi

Committee Member 1

Tong Liu

Committee Member 2

David Goldberg

Abstract

For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\in\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\in\g_{a}$, we construct packets of supercuspidal representations $\{\pi_{v,\rho}\}$ as well as discrete Langlands parameters $\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\pi_{v,\rho}$ and $\varphi_{v}$ satisfy both sides of the formal degree conjecture.